chapter 5 aggregation of small...
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CHAPTER 5
AGGREGATION OF SMALL PARTICLES
5.1 Introduction
5.1.1 Van der Waals attraction
5.1.2 Electrostatic repulsion
5.1.3 Diffusion limited aggregation
5.1.4 Reaction limited aggregation
5.1.5 Characterisation of the aggregates
5.1.6 Work included in this chapter
5.2 Aggregation of microclusters of sulphur
5.2.1 Introduction
5.2.2 Experiment and Observation
5.2.3 Discussion
5.3 Aggregation of microclusters of silver
5.3.1 Introduction
5.3.2 Experiment and Observation
5.3.3 Discussion
5.4 Aggregation of microclusters of silver
iodide and mercuric iodide
5.4.1 Introduction
5.4.2 Experiment and Observation
5.4.3 Discussion
5.5 Conclusion
References
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5.1 Introduction
Understanding kinetic aggregation of small
particles to form clusters and the study of the structure of
these clusters has been the prime goal in the field of
colloid physics for many years. The interest in this field
was aroused not only due to the fact that colloid
aggregation represents one of the major applications and
experimental tests of modern statistical theories of kinetic
growth, but recent developments including computer
simulations (1,2) have made it feasible to quantitatively
characterize the aggregates despite their very random and
disordered appearance. The random, tenuous clusters that are
produced when colloids aggregate, exhibit dilation symmetry
and can be termed as fractals ( 3 ) . Since cluster aggregation
is a kinetic non-equlibrium growth process, the structure of
the aggregates is inherently related to dynamics of
aggregation.
The particles dispersed in a liquid phase will be
undergoing Brownian notion and will be continually colliding
with one another. There should be a protective mechanism to
prevent aggregation and to retain the individuality of the
particles. The protection may be achieved through
electrostatic stabilization or through steric stabilization.
In the case of electrostatic stabilization the electrical
protection may be destroyed by an increase in the
electrolyte content of the solution at a fairly sharp
concentration. All electrolytes have this effect but counter
ions of high charge numbers are much more effective than
those of low valence. This valance effect is known as the
rule of Schulze (4) and Hardy ( 5 ) . A sterically protected
suspension may be caused to flocculate by the addition of a
non-solvent for the protecting molecules. These protective
mechanisms can only slow down the process of aggregation but
cannot prevent it. The structure of the aggregates depends
strongly on the mechanism of aggregation. If the repulsion
between particles in a suspension is significant, the
particles will coagulate only very slowly but when they do
so they are observed to form very compact structures with
little entrapped solvent. When the repulsion is not
significant, the clusters stick to one another immediately
and irreversibly upon collision and the aggregation rate is
determined by the diffusion of the clusters. The key to the
traditional understanding of both colloid stability and
aggregation of small particles dispersed in a liquid medium
is in the determination of the energy of interaction between
two colloid particles as a function of their center-to-
centre separation (6). The energy of interaction between
particles may arise due to van der Waals attraction or by
electrostatic repulsion.
5.1.1 Van der Waals attraction
The van der Waals forces between the atoms in two
approaching particles are to some extent additive and the
overall effect is an attractive force of quite long range.
The idea has been worked out by De Boer (7) and especially
by Hamaker (8). According to the widely used DLVO theory
(9,10,11), The attractive van der Waals interaction between
two spherical particles is
where A is the Hamaker constant, r is the separation of the
centres and a is the sphere radius
5.1.2 Electrostatic Repulsion
Suspensions of a solid phase in a liquid medium can
be stable over a long period of time if the particles repel
one another strongly enough to overcome the van der Waals
attraction. Electrostatic repulsion if exists can be strong
enough and can have a long enough range to do the job. In
the case of electrostatic stabilization the repulsive
screened coulomb forces is
where Z is the charge per sphere, €the dielectric constant
of the solvent K is the inverse screening length and n the
total number of ions in solution
The potential energy due to van der Waal's effect
between two colloidal particles of the same material
immersed in a fluid is negative. The repulsive force due to
Coulombic interactions between particles lead to a positive
potential energy. There is a primary and secondary minimum
due to the attraction with a steep barrier between them. It
is well established that the height of the barrier and the
depth of the secondary minimum play a critical role in
determining the extent of particle aggregation. Thus the
energy barrier height Eb of width K-l is the origin of the
stability of a dispersion aganist aggregation. In a
diffusion induced collision, two particles will approach
- 1 to within K , and will overcome the energy barrier and
stick together with a probability P+exp(-Eb/kBT) where kg
is the Boltzmann constant and T is the temperature.
This type of an approach can be used to determine the
initial rate of aggregation. The subsequent
aggregation kinetics are more complicated as the
clusters themselves also diffuse and grow. The mechanism
of aggregation observed in fresh and aged suspensions will
therefore be different and fall into two universal regimes,
namely diffusion limited aggregation(DLA) and reaction
limited aggregation(RLA).
5.1.3 Diffusion Limited Aggregation
When Eb << k T where kB is the Boltzmann constant, B
the aggregation rate is maximum and particles stick to one
another quickly and irreversibly upon collisions. The
aggregation is limited only by the diffusion of particles or
small clusters of particles and this regime named diffusion
limited aggregation (6,121 forms the first universal regime
of kinetic aggregation. A general feature of this kind of
aggregation appears to be the dilation symmetry exhibited by
the resultant clusters, whether they are formed by accretion
of single particles or by cluster-cluster aggregation. The
tenuous, highly disordered structures of the clusters can be
quantitatively characterized as fractals. The fractal
dimension of the cluster aggregates is experimentally found
( 6 ) to be df = 1.75+ - 0.05, which is in excellent agreement
with the fractal dimension obtained from computer
simulations of the cluster-cluster aggregation models ( 6 ) .
The fractal dimension remains the same when the diffusivity
of the clusters is taken to be independant of the mass(l3).
The fractal dimension is also not sensitive to the form of
cluster mass distribution, remaining unchanged whether the
aggregation occurs in a system of equal sized clusters (14)
or in polydisperse distributions (15). Furthermore, small
structural reorganisations to form a more stable
configuration after the clusters stick do not appear to
change the fractal dimension significantly (6).
5.1.4 Reaction Limited Aggregation
When Eb > KBT the rate of aggregation is many
orders of magnitude less than that for DLA. In this case the
rate limiting step in the kinetics is the actual formation
of a bond and we label this rpgime reaction limited
aggregation (6). In the RLA regime, the structure of the
clusters, as determined by their fractal dimension, the
aggregation dynamics, and the cluster mass distributions all
change dramatically from the DLA behaviour. The large
clusters formed by RLA have a much more dense and compact
appearance than that of the clusters formed by DLA. This may
be due to the reason that the clusters will be able to
interpenetrate one another to a greater degree than for DLA,
leading to an increased fractal dimension (df=2.05+0.1) for
the clusters (6). The bonds once they are formed, are very
strong and rigid. This rigidity along with the complex
geometry of the clusters, will ensure that the aggregates
are still quite tenuous and that their structure is still
fractal.
Thus the two universl regimes-DLA and RLA- appear
to be sufficient to describe the mechanisms of homogenous
aggregation of a large number of colloidal systems
5.1.5 Characterisation of the Aggregates
The best way to study the structure of the highly
dispersed colloidal aggregates would be to observe then in
three dimensions. The very small size of the particles makes
it necessary to use transmission electron microscope(TEM) to
attain sufficient resolution to measure the structure down
to length scales of the order of the individual particles
( 6 ) . Analyses of aggregates using'TEM has the disadvantage
that the TEN image is a two dimensional projection of the
three dimensional cluster and that the cluster have to be
removed from the liquid phase and dried, a process that may
distort the structure. Still TEM imaging is the most direct
and convenient method to actually see and analyse the
structure of aggregates and it has been shown that fractal
dimension obtained by TEM analysis corresponds to that of
the cluster in solution (6).
5.1.6 Work Included in this Chapter
In this chapter, the study of aggregation of
microclusters of certain materials using TEN and electron
diffraction are discussed. Section 1 deals with the study of
aggregation of microclusters of sulphur dispersed in water
methanol mixture, Section 2 consists of the investigation of
the mechanism of aggregation observed in Ag colloids in the
presence of a stabiliser and in Section 3, the aggregation
found in fresh and aged samples of microclusters of AgI and
HgIZ are discussed.
SECTION 1
5.2 Aggregation of Microclusters of Sulphur
5.2.1 Introduction
The process of agregation of small particles to
form larger clusters and the structure that result are
important technologically and scientifically. All of our
knowledge of the growth of these clusters has come from
computer simulations (1,2,14,15) which have suggested that
the resultant structures exhibit scale invariance and can be
termed as fractals. Despite the accumulation of the wealth
of theoretical results on the kinetics of aggregation,
experimental work that can test the validity of modern
theories have been rather sparse. Forrest and Witten (16)
have analysed aggregation of metallic smoke particles and
Weitz and Oliveria (17) investigated aggregates of uniform
aqueous colloids of gold by TEM. Schafer et a1 (18) have
reported TEM analyses of silica particles. The structures
formed in these cases were highly ramified exhibiting a
scale invariance and are described as fractals.
This section consists of a study of aggregation of
colloidal suspension of sulphur particles by TEM and
electron diffraction. The aggregates formed have been found
to be random, tenuous and could be termed as fractals. The
electron diffraction patterns of the aggregates are found to
be spotty indicating that the aggregating particles are
crystalline (21,221. The electron diffraction photographs
have been used to study the mechanism of aggregation.
5.2.2 Experiment and Observation
Suspensions of small particles of sulphur used in
this work were prepared by quickly adding measured quantity
of a saturated solution of flours of sulphur in methanol at
constant temperature in to doubly distilled water (23).
Suspensions of two different concentrations (ratio of
distilled water to sulphur solution) were used for the
present study. The suspension of 2:1 concentration contained
0.113 gm of sulphur per litre and the 4:l concentration
contained 0.056 gm of sulphur per litre of the suspension. A
drop of the freshly prepared suspension of sulphur was
placed on the TEM grid and the liquid phase was allowed to
evaporate. The structure of the sulphur clusters were
examined using a PHILIPS EM 301 TEM. By examining the full
area of the TEM grid, clusters of widely varying degree of
aggregation could be found and photographed. The same
microscope but now in the electron diffraction mode was used
for the determination of crystallinity of the sulphur
particles and selected area electron diffraction photographs
were taken. The samples were allowed to age at constant
temperature for 24 hours and these were also subjected to
TEM and electron diffraction studies to determine the effect
of aging on the extent of aggregation of the particles.
Electron micrographs of fresh (Figs.5.1 and 5.3) and aged
(Figs.5.2 and 5.4) samples are reproduced to show the
structure of the aggregates. Figures 5.5,5.7 and 5.6,5.8 are
the electron diffraction photographs of aggregates in fresh
and aged samples respectively.
5.2.3 Discussion
The random, tenuous clusters that are produced
when colloids aggregate can be quantitatively characterised
as DLA or RLA despite their very disordered appearance-It
has been shown that the aggregates produced through the
reaction limited and diffusion limited process show dilation
symmetry and can be termed as fractals (6). The random
aggregates of sulphur particles produced in fresh as well as
aged samples in the present study must also be self similar
Figure Captions
Fig.5.1 - 5.4 Electron rn-icrography of suspensions of
small particles of sulphur.
Fig.5.1 Fresh sample (Con. 2:l)
Fig.5.2 Aged sample (Con. 2:l)
Fig.5.3 Fresh sample (Con. 4:l)
Pig.5.4 Aged sample (Con. 4:l)
Figure Captions
Fig.5.5 - 5.8 Electron diffraction photographs of
suspensions of small particles of sulphur.
Fig.5.5 Fresh sample (con. 2:l)
Fig.5.6 Aged sample (Con. 2:l)
Fig.5.7 Fresh sample (Con. 4:l) '
Fig.5.8 Aged sample (Con. 4:l)
and could be termed fractals since aggregation has been
amply well shown to be describable by DLA and RLA regimes
( 6 ) .
Theoretical and experimental studies reported in
the literature indicate that the clusters themseleves may
diffuse via Brownian motion and growth occurs when two
clusters aggregate. These cluster-cluster aggregation
models (6) are better representation of the actual
experimental situation than the attachment of particles one
by one on a growing aggregate. Also in the RLA regime in
which the bond formation is the rate limiting step, this
model may even lead to chemical reaction upon aggregation.
Each tiny cluster getting added to a growing cluster, made
up of crystalline particles and the crystalline nature
of the particles forming a tiny cluster may not hamper
the formation of aggregates exhibiting fractal structure
( 2 0 ) . The TEM micrographs (Figs.5.1 to 5.4) show irregularly
shaped, ramified structures for fresh and aged samples of
suspensions of sulphur particles. The structure of
aggregates of sulphur observed in fresh samples should be
more open and must fall in the DLA regime while structure of
aggregates of aged samples should be more dense and should
fall in the RLA regime. The electron diffraction
photographs of the structures formed in fresh samples of low
concentrations show (Fig.5.7) limited number of spots
indicating only thin packing of crystalline particles,
there by indicating a role of DLA. Electron diffraction
photographs for aged samples (Fig.5.8) of low concentrations
show much larger number of spots (almost rings) indicating
close packing of crystalline particles. This indicates that
aggregates formed in aged samples of low concentration must
be more dense and must be formed through RLA mechanism. At
high concentrations (-?:I) open structures are formed
initially by DLA (Fig.5.5) and structures formed after 24
hours indicate an extreme case of close packing of
particles, resulting in the formation of a poly crystalline
mass with a limited number of crystallites (21,22). This is
evident from the very limited number of diffraction spots
(Fig.5. 6).
SECTION 2
5.3 Aggregation of Small Particles of Silver
5.3.1 Introduction
Metal colloids have been known for a long time and
are of great interest due to their technological, industrial
and medicinal applications. Colloidal gold is the most
traditional and widely studied colloid and was known at
least as far back as the twelth century. Faraday's
scientific studies of colloidal gold was instrumental in the
establishment of the discipline of colloid science. Many of
the concepts of colloid science, especially the stability of
colloids, were tested using colloidal gold. Colloidal silver
also have been known long ago and prepared by various
methods (24-261, of which the preparation of Carey Lea
silver colloid dates back to 1889. Colloidal silver have
been studied mainly for their optical properties (27-30).
These colloids are also of interest in the areas of
catalysis, especially when free organic radicles in solution
are involved. More recently they gained interest with the
surface enhanced Raman scattering technique(SERS1 for the
study of molecules adsorbed at the surface of colloidal
particles. These studies emphasized that the various
properties of small particles of silver are influenced by
the size and shape of particles and more specially by their
aggregation state. In this work an attempt has been made to
characterise through electron microscopy the cluster
aggregation observed in silver colloids produced by Bredigs
method.
5.3.2 Experiment and Observation
Silver suspension used for the present study were
prepared by Bredis's method (23,31) as discribed in section
2 of chapter 4. The resulting suspension was filtered to
remove coarser particles and kept undisturbed for two days
for the particles to aggregate. The particles in the
suspension were then subjected to TEM and electron
diffraction studies to determine the effect of aging on the
extent of aggre~ation. The TEN micrographs of the aggregates
(see Fig.4.2 of chapter 4) exhibits the tenuous ramified
appearance characteristically observed for fractal
aggregates. The electron diffraction photographs (see Fig
4.3 of chapter 4) show characterstic diffraction rings
observed for crystalline material.
5.3.3 Discussion
The electron micrographs of aggregates of silver
show the random tenuous nature exhibited by fractal
aggregates. The aggregates formed when silver particles
flocculate, can be due to DLA or RLA just as in the case of
sulphur clusters discussed in section 1 of this chapter.
Since no electrolyte is added to initiate aggregation in the
silver suspension, the necessary cocdition for DLA, ie
Eb<<kgT may not be satisfied and the aggregation mechanism
may not in general be DLA. Even though the probability of
formation of clusters through DLA are small the chance for
the presence of aggregates formed through DLA cannot be
discarded, since at the time of prepar~tion of the colloid
the formation of clusters through DLA are probable.
In the case of silver colloid, the surface adsorbed
ions cause the silver particles to be highly charged and
the ionic strength of the solution creates a Debye-Huckel
screening length of few atomic distances. The resulting
double layer interaction between the particles makes the
suspension very stable against aggregation. Since the
repulsive double layer interaction is very strong (Eb>kgT),
the clusters will not stick to one another immediately on
collision, but they may do so through the formation of a
bond. Thus the rate limiting step in the kinetics of
aggregation is the actual formation of a bond and we label
this regime of aggregation as reaction limited aggregation
( 6 ) . The electron diffraction pattern of the aggregates of
silver show the characteristic diffraction rings (see Fig
4.3 of chapter 4). This indicates that the particles forming
the aggregates are crystalline and they are packed closely
and are much dense. It is established through experimental
observations that the large clusters formed by RLA have a
much more dense compact appearance (6). This result together
with the results of the present study shoe that the
aggregation produced in aged silver suspension may fall
under the RLA regime.
SECTION 3
5.4 Aggregation of Microclusters of AgI and Hg12
5.4.1 Introduction
Though the aggregation of metal clusters have been
studied widely (16-la), the investigation of aggregation of
clusters of inorganic compounds are rather few (32). Study
of the dynamics of aggregation in inorganic colloids will
provide a better understanding of the physical properties of
the aggregates. The importance of silver iodide (32) in
photographic processes has led to extensive investigation of
their properties and intense interest in the mechanism of
aggregation. Colloidal Hg12 is also a material of wide
industrial applications. In this section, the aggregation
dynamics observed in fresh and aged samples of colloidal AgI
and Hg12 are discussed.
5.4.2 Experilnent and Observation
Aqueous suspensions of AgI and Hg12 used in the
present work were prepared as discussed in section 2 of
chapter 4. Fresh and aged samples of the suspensions of AgI
and Hg12 were subjected to TEM and electron diffraction
studies. A well defined continuous ring structure was
observed in the electron diffraction pattern of aged samples
of Hg12 (see Fig.4.8) while fresh samples indicate a spotty
pattern (see Fig.4.7 ) . Electron diffraction pattern of
fresh suspensions of AgI indicates a spotty (see Fig.4.9)
behavieur while aged samples show rings with a limited
number of bright spots (see Fig.4.10).
5.4.3 Discussion
The TEM micrographs of clusters of AgI and Hg12
(see Figs.4.5 and 4.6) indicate the state of aqgregation in
these clusters. The stability of AgI and HgIg suspensions
are found to be different. AgI suspension is found to be
moderately stable while the suspension of Hg12 flocculates
within a very short time after preparation. The aggregation
dynamics observed in fresh samples of the above suspensions
falls in the DLA regime, since the probability of formation
of clusters through DLA is large at the tine of
preparation of the suspension. It is established by
experimental observations that the aggregates formed through
DLA are less densly packed (6). The electron diffraction
pattern of fresh samples of AgI (see Fig.4.9) indicate thin
packing of crytalline material and suggests that the
aggregation dynamics observed falls in the DLA regime.
In the case of aged samples of AgI, the energy
barrier between particles is significant and particles stick
to each other only by the formation of a bond. The electron
diffraction pattern of aged samples of AgI (see Fig.4.10)
shows almost continuous diffraction rings indicating a
close packing of crystalline particles in the aggregates and
thereby indicating that the mechanism of aggregation falls
in the RLA regime.
The Hg12 suspension which is very unstable
aggregates within a short time after the preparation. No
electrolyte is required to initiate aggregation. In this
case E <<k T and the aggregation is limited only by the b B
diffusion of particles. Thus in Hg12. the aggregation
observed in fresh and aged samples are the same and falls in
the DLA regime (see Figs.4.7 and 4.8).
5.5 Conclusion
The process of aggregation of microclusters has
been analysed by TEM and electron diffraction. The
aggregates formed exhibit a fractal behaviour. The
mechanism of aggregation observed in fresh and aged
suspensions may fall under the regimes of diffusion limited
aggregation or reaction limited aggregation according as the
energy of interaction between the clusters.
References
1. T.A.Witten and L.M. Sander, Phys.Rev.B.27(1983)5686.
2. T.A.Witten and L.M.Sander, Phys.Rev.Lett.47(1981)1400
3. B.B.Mandlebrot, The Fractal Geometry of Nature Freeman,
Sanfrancisco, 1982.
4. H.Schulz, J.Prakt. Chem. (2) 25(1882)431.
ibid (2) 27(1883)320.
5. W.B.Hardy, Proc.Roy.Soc.London 66(1900)110.
6. D.A.Weitz, M.Y.Lin and J.S.Huang, Physics of Complex and
Supermolecular fluids Ed.Samuel.A.Safran and Noel.A.Clark
John Meily and sons, 1987, p-509
7. J.H.Boer,Trans.Faraday.Soc. 32(1936)21.
8. H.C.Hamaker, Rev.Trav.Chim 55(1936)1015, ibid 56(1937)727
Physica 4(1937)1058.
E.J.W.Verwey and T.J.T.Overbeek Theory of the stability of
Lyophobic Colloids Elsevier, Amsterdam, 1948.
J.Visser, Adv.Coll.Int.Sci. 3(1972)351.
J.O'M.Bockris and A.K.N.Reddy, Modern Electrochemistry,
Plenum Press, New York, 1970.
D.A.Weitz, J.S.Huang,PI.Y.Lin and J.Sung Phys.Rev.Lett.53
(198311657.
P.Meakin, Phys.Rev.B 29(1984)2930.
M.Klob,R.Botet and R.Jullian, Phys.Rev.Lett.51(1983)1123.
P.Meakin, Phys.Rev.Lett. 51(1983)1119.
S.R.Forrest and T.A.Witten, J.Phys.A 12(1979)109.
17. D.A.Meitz and M.Oliveria, Phys.Rev.Lett 52(1984)1433.
18. D.W.Schawfer and J.E.Martin, Phys.Rev.Lett.52(1984)2371.
19. R.F.Voss, R.B.Laibowitz and E.I.Allessandrini, Phys.Rev.
Lett.52(1984)2371.
20. A.J.Hurd, Physics of Complex and Supermolecular fluids
Ed.Samue1.A.Safran and Noel.A.Clark, John Weily and
sons 1987,p-493.
21. J.Grundy and G.A.Jones, Electron Microscopy in the Study
of Materials Ed.Prof.Bryan R-Coles, Edward Arnold, 1976.
22. M.Abdulkhadar and K.C.George, Pramana-J-Phys. 37(1991)321
23. H.B.Weiser, A Text book of Colloid Chemistry, John
Weily and Sons Inc. New York, 1949, p-146.
24. M.Carey Lea, Amer.J.Sci. 37(1889)476.
25. A.Henglein, J.Phys.Chem.83(1979)2209.
26. J.A.Creighton, G.C.Blatch ord and M.G.Albrecht,
J.Chem.Soc.Faraday Trans.11 15(1979)790.
27. R.H.Morris and L.F.Collins, J.Chem.Phys.41(1964)3357.
28. D.C.Skillman and C.R.Berry, J.Chem.Phys 48(1968)3297.
29. S.D.Stookey, G.H.Beai1 and H.E.Pierson, J.Photogr.Sci.26
(1978)209.
30. G.C.Papavassilion, Prog.Solid State Chern. 12(1980)185.
31. M.D.Jirgensons and M.E Straumanis, "A Text Book of
Colloid Chemistry", Pergamon Press, London ,1964.
32. D.Hayes, K.H.Schmidt and D.Meise1, J.Phys.Chem.
93(1989)6100.